We will start with the representation theory of a particular finite group, which yields Kloosterman sum identities, a concrete family of commuting hermitian matrices with a number of ''magical'' combinatorial properties and some related multigraphs which display Ramanujan-like behavior. Prior knowledge of the technical terms in the above sentence will not be required. This is joint work with Patrick S. Fleming and Stephan Ramon Garcia, and will mainly be an exposition of our recent paper with the same title (Journal of Number Theory 131 (2011), pp.661–680).